Four staff members at a certain company worked on a project.

SOLUTION

Four staff members at a certain company worked on a project. The amounts of time that the four staff members worked on the project were in the ratio 2 to 3 to 5 to 6. If one of the four staff members worked on the project for 30 hours, which of the following CANNOT be the total number of hours that the four staff members worked on the project?

(A) 80
(B) 96
(C) 160
(D) 192
(E) 240

A:B:C:D=2x:3x:5x:6x, for some positive number x. Total time 2x+3x+5x+6x=16x.

If 2x = 30 then 16x = 240;
If 3x = 30 then 16x = 160;
If 5x = 30 then 16x = 96;
If 6x = 30 then 16x = 80;

Only answer choices which is not obtained is 192.

Answer: D.
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Let the time taken is 2x, 3x , 5x & 6x
Total time taken 16x
Any one of 2x, 3x , 5x & 6x equals 30 .
So 16x can take any of the below mentioned values -
30*16/2 , 30*16/3, 30*16/5 , 30*16/6
240 , 160, 96, 80
Answer D

Let the time taken as 2x, 3x , 5x & 6x
Total time taken 16x
Any one of 2x, 3x , 5x & 6x equals 30 and x can be 15, 10, 6 and 5 respectively.
Now for all values of X (15,10,6 & 5) 16x will be
= 16*15 = 240 (E)
= 16*10 = 160 (C)
= 16*6 = 96 (B)
= 16*5 =80 (A)

Hence Answer D

Ohh 13 the edition question luk little trickier than 12th...i didnt buy 13th yet..

well.. +1 to all above me

very nice question bunuel ..

2x, 3x, 5x, 6x...sum=16x

we r taking X as total no of hours..

2/16x=30 ...x=240

3/16x=30=then x can be =160

5/16x= 30 ...then x can be =96

6/16x= 30..then x can be =80..

D is the only choice which can not X value..
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Four members worked in ration 2:3:5:6, hence as everyone mentioned, individual work could be taken as 2x, 3x,5x, and 6x. Also this gives us total work as 16x.
But we are told that one of these individual works is 30hrs. hence, possible scenarios, if
(1)2x =30 => 16x = 240 (2) 3x =30 => 16x = 160 (3) 5x =30 => 16x = 96 (4) 6x =30 => 16x = 80
Hence Answer is D 192 which can not be any of these.
Another alternate is to backsolve,
for options A to E, Answer/16 should give us a multiplication factor (which is denoted by x in first solution). Since this multiplication factor should be present for individual work also, 30 should be divisible by this to give individual work ratio of any out of 2,3,5,6.
eg. 80/16 =5 and 30/5 =6 or 240/16=15 and 30/15=2, but 192/16=12 and 30/12 =2.5 (not one of the ratios)
This leaves us with choice D again.

Hi Bunuel,

If we change this question to say that the ratios are still the same i.e 2, 3, 5 and 6 but the prompt says that the the sum of the hours worked by two of the workers is 121 and then we are asked to find the sum of total hours worked by all the workers. Would this be still a valid variation provided we restrict the number of hours in integers only?

Thanks in advance.

Yes.

Given: A:B:C:D=2x:3x:5x:6x, for some positive integer x and the sum of the hours worked by two of the workers is 121.

Since the only sum which gives integer value for x is 5x+6x=121 --> x=11, then total time is 16x=16*11.

Hope it helps.
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Given Ratios- 2:3:5:6
2x+3x+4x+5x=16x
lets check one by one with ACs, and when we come to D;
16x=192
=>x=12
if you put x= 12 in any individual's value (2x,3x,5x,6x) 30 can not be acheived.

Answer : D

Attached is a visual that should help.

We are given that the amounts of time that the four members worked on the project were in the ratio 2 to 3 to 5 to 6. A straightforward approach is to create a ratio with x multipliers. The ratio becomes: 2x : 3x : 5x : 6x, in which 2x was person 1’s time, 3x was person 2’s time, 5x was person 3’s time, and 6x was person 4’s time.

From this information, we can determine that the total time worked by all the members is the sum of our ratios: 2x + 3x + 5x + 6x = 16x.

We are also given that one of the members worked for 30 hours. Thus, we can create 4 different equations to get 4 different possible x values.

Option 1) If Person 1 was the individual who worked 30 hours, then 2x = 30 and x = 15

Option 2) If Person 2 was the individual who worked 30 hours, then 3x = 30 and x = 10

Option 3) If Person 3 was the individual who worked 30 hours, then 5x = 30 and x = 6

Option 4) If Person 4 was the individual who worked 30 hours, then 6x = 30 and x = 5

The above results show the 4 different options for the total number of hours an individual staff member worked.

Now, remember that the entire group worked for 16x hours. We substitute each of the 4 possible values for x into this expression:

Option 1: 16x = (16)(15) = 240 hours

Option 2: 16x = (16)(10) = 160 hours

Option 3: 16x = (16)(6) = 96 hours

Option 4: 16x = (16)(5) = 80 hours

The only value that we did not get was 192 hours, so D is the correct answer.

Answer: D
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Brute Force:
You know the ratio is 2x:3x:5x:6x =16x
Now you can set 16x equal to all the answer options and see which one when you calculate through the options yields 30. So each option except one does contain one member that worked 30 hours.
For A) x yields 5 so 6*5=30 -->wrong
B) x yields 6 5*6= 30 -->wrong
C) x yields 10 3*10=30 --> wrong
D) x yields 12 when you calculate through you see nothing yields 30 --> bingo
E) x yields 15 2*15 =30 -->wrong
The moment you figured out D does not yield a 30 you can stop working

Concept Involved

Take any Ratio: \(\frac{A}{B}\) = \(\frac{3}{4}\)
Becomes \(\frac{A}{B}\) = \(\frac{3x}{4x}\)

Since its a Ratio we do not know the total elements, values represent. But we do know this
Total = 3x +4x= 7x
It will be some multiple of 7

Using this concept as iteration we can
Total for entire staff as : 2x + 3x + 5x + 6x= 16x
Total will be some multiple of sixteen

Since we have total hours (30) for one of the staff members, we will get four different multipliers.
2x=30 : x=15
3x=30 : x=10
5x=30 : x=6
6x=30 : x=5

Using these multipliers By Trial and error you would quickly realise Answer is D

I tested each case to arrive to the answer.
Case 1)
2:3:5:6 (assume 30 h is the least number of hours worked, then multiple is 15)
30:45:75:95, total number is 240 (cross E)
Case 2) (assume 30 h is the second least number of hours worked, then multiple is 10)
2:3:5:6
20:30:50:60, total number of hours is 160 (cross C)
Case 3) (assume 30 h is the second greatest number of hours worked, then multiple is 6)
2:3:5:6
12:18:30:36, total number of hours is 96 (cross B)
Case 4) (assume 30 h is the greatest number of hours worked, then multiple is 5)
2:3:5:6
10:15:25:30, total number of hours is 80 (cross A).
Now, we are left with D, which is the correct answer

Hi All,

We’re told that four staff members spent time working on a project in the ratio of 2:3:5:6 and that ONE of the staff members worked 30 hours. We’re asked which of the following could NOT be the total number of hours worked by the four members.

Since this question involves ratios, it’s worth noting that ratios are all about MULTIPLES. We’ll have to do more work than normal on this question (since we’ll have to calculate more than one possible outcome, but the math involved is just basic Multiplication and Arithmetic - and if you're paying attention to the patterns involved, you don't actually have to calculate every possible outcome...).

IF… the first person worked 30 hours…. Then 30 is “15 times” 2, so each of the other numbers in the ratio needs to be multiplied by 15. The four numbers would be…

30 + 45 + 75 + 90 = 240
Eliminate Answer E

IF… the second person worked 30 hours…. Then 30 is “10 times” 3, so each of the other numbers in the ratio needs to be multiplied by 10. The four numbers would then be…

20 + 30 + 50 + 60 = 160
Eliminate Answer C

At this point, you might notice that the total number of hours dropped – and we have ‘jumped past’ Answer D. Since the total is likely to continuing dropping as we continue doing our calculations, it’s likely that D is the correct answer. If you don’t recognize this pattern, then you can continue working (and you’ll eliminate the other 2 answers without too much trouble).

IF… the third person worked 30 hours…. Then 30 is “6 times” 5, so each of the other numbers in the ratio needs to be multiplied by 6. The four numbers would then be…

12 + 18 + 30 + 36 = 96
Eliminate Answer B

IF… the fourth person worked 30 hours…. Then 30 is “5 times” 6, so each of the other numbers in the ratio needs to be multiplied by 5. The four numbers would then be…

10 + 15 + 25 + 30 =80
Eliminate Answer A

Final Answer:

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